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Worksheet: Limits of Composite Functions

Q1:

Suppose and What can be said of the continuity of 𝑔 ( 𝑓 ( π‘₯ ) ) at π‘₯ = βˆ’ 3 ?

  • AThe function is discontinuous at π‘₯ = βˆ’ 3 because l i m π‘₯ β†’ βˆ’ 3 𝑔 ( 𝑓 ( π‘₯ ) ) does not exist.
  • BThe function is continuous at π‘₯ = βˆ’ 3 .
  • CThe function is discontinuous at π‘₯ = βˆ’ 3 because 𝑔 ( 𝑓 ( βˆ’ 3 ) ) is undefined.
  • DThe function is discontinuous at π‘₯ = βˆ’ 3 because l i m π‘₯ β†’ βˆ’ 3 𝑔 ( 𝑓 ( π‘₯ ) ) β‰  𝑔 ( 𝑓 ( βˆ’ 3 ) ) .

Q2:

Suppose and What can be said of the continuity of 𝑔 ( 𝑓 ( π‘₯ ) ) at π‘₯ = βˆ’ 3 ?

  • AThe function is discontinuous at π‘₯ = βˆ’ 3 because l i m π‘₯ β†’ βˆ’ 3 𝑔 ( 𝑓 ( π‘₯ ) ) does not exist.
  • BThe function is continuous at π‘₯ = βˆ’ 3 .
  • CThe function is discontinuous at π‘₯ = βˆ’ 3 because 𝑔 ( 𝑓 ( βˆ’ 3 ) ) is undefined.
  • DThe function is discontinuous at π‘₯ = βˆ’ 3 because l i m π‘₯ β†’ βˆ’ 3 𝑔 ( 𝑓 ( π‘₯ ) ) β‰  𝑔 ( 𝑓 ( βˆ’ 3 ) ) .